# LAB2GO Wiki

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playground:gabriele_dv_trafelli2021

## Positron driven muon source for a muon collider

### Introduction

As far as the muon bunch intensity is concerned, the number of $\mu^{+}\mu^{-}$ pairs produced per positron bunch on target is: $$n\left(\mu^{+}\mu^{-}\right)=n^{+}\rho^{-}l\sigma\left(\mu^{+}\mu^{-}\right)$$ where $n^{+}$ is the number of $e^{+}$ in the bunch, $p^{-}$ is the electron density in the medium, $l$ is the thickness of the target, and $(sigma\left(\mu^{+}\mu^{-}\right)$ is the muon pairs production cross section.The $e^{+}e^{-} → \mu^{+}\mu^{-}$ cross section as a function of the positron beam energy is given in the next figure.

### Positron source

The $e^{+}$ source has to provide trains of 1000 bunches with 5x$10^{11}$ $\frac{e^{+}}{bunch}$ to inject in the Damping Ring at 5GeV. Embedded Source For each positron on the primary 3 mm Be target there are:

• 0.11 photons hitting the W target
• 0.65 $e^{+}$ coming out of the 5X0W target.
Parameter Value
$\epsilon_{n,y}$ $7.9 \times10^{3}$mm mrad
$E$ $\simeq 190$ MeV
$\Delta_{E}$ $4.9 \times 10^{4}$ keV

Commento di Fausto C.
Hai dimenticato di andare a capo dopo Embedded Source, qualche imprecisione nel LateX e non hai scritto la nota, ma per il resto molto bene! Ti segno i 30m di lavoro a casa per aver completato la pagina!

playground/gabriele_dv_trafelli2021.txt · Ultima modifica: 2021/04/12 07:17 da fausto.casaburo